In digital communications it is sometimes desirable to avoid transmission at certain Frequencies in the transmission spectrum. It is usually necessary to do so in order to avoid undesirable distortion which might result if communications signals use certain frequency components. The presence of such distortion can lead to unnecessary performance degradation.
To avoid transmission at the undesirable frequencies in the spectrum it is necessary to shape the transmission spectrum of the transmitted signals accordingly. The principles of spectral shaping are conveniently described, for example, in U.S. Pat. No. 5,818,879, entitled “Device, System and Method for Spectrally Shaping Transmitted Data Signals”. Previously proposed schemes for spectral shaping achieve the desired result by the use of redundancy. One such scheme is the trellis based spectral shaping which has been proposed for the V.90 standard to be ratified by the ITU-T International Telecommunication Union: ‘A digital modern and analogue modem pair for use on the public switched telephone network (PSTN) at data signalling rates of up to 56 000 bit/s downstream and up to 33 600 bit/s upstream’ ITU-T recommendation V.90, September 1998, Geneva, Switzerland. This scheme uses a convolutional code with two states and provides significant gain.